combo.py

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# Copyright (C) 2002-2020 CERN for the benefit of the ATLAS collaboration
 
#
# $Id: combo.py,v 1.3 2005-05-12 16:36:59 ssnyder Exp $
# File: combo.py
# Created: sss, Mar 2005, from http://aspn.activestate.com/.
# Purpose: Generators for combinations and permutations.
#
 
 
"""Generators for combinations and permutations.
 
This module contains functions for
generating all combinations and permutations from a list of
items.  These functions return generators, so you may iterate
over them or retrieve successive values with
next().  Given a sequence items,
you can iterate over the list of unique pairwise combinations with
 
   for (i1, i2) in combo.xuniqueCombinations (items, 2):
 
The functions contained in this module are:
 
  combinations(items,n)
    Yields all unique subsequences of length n from items.
 
  all_combinations(items,n)
    Similar, but differences in ordering are considered significant.
    For example, all_combinations([1,2,3],2) will yield both [1,2] and [2,1].
 
  permutations(items)
    Yields all permutations of items.
    Equivalent to all_combinations(items,len(items)).
 
  selections(items,n)
    Returns all possible ways of picking n items from
    items, where any given item may be picked multiple times.
"""
 
from builtins import range
__version__ = "1.0"
 
"""combo.py
Generators for calculating a) the permutations of a sequence and
b) the combinations and selections of a number of elements from a
sequence. Uses Python 2.2 generators.
 
Similar solutions found also in comp.lang.python
 
Keywords: generator, combination, permutation, selection
 
See also: http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/105962
See also: http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/66463
See also: http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/66465
"""
 
def all_combinations(items, n):
    """Return all subsequences of length n from items.
Differences in ordering are considered significant.
For example, all_combinations([1,2,3],2) will yield both [1,2] and [2,1].
 
>>> for c in all_combinations(['l','o','v','e'],2):
...   print (''.join(c))
lo
lv
le
ol
ov
oe
vl
vo
ve
el
eo
ev
"""
    if n==0:
        yield []
    else:
        for i in range(len(items)):
            for cc in all_combinations(items[:i]+items[i+1:],n-1):
                yield [items[i]]+cc
 
def combinations(items, n):
    """Yields all unique subsequences of length n from items.
 
>>> for uc in combinations(['l','o','v','e'],2):
...   print (''.join(uc))
lo
lv
le
ov
oe
ve
"""
    if n==0:
        yield []
    else:
        for i in range(len(items)):
            for cc in combinations(items[i+1:],n-1):
                yield [items[i]]+cc
            
def selections(items, n):
    """Returns all possible ways of picking n items from
items, where any given item may be picked multiple times.
 
>>> for s in selections(['l','o','v','e'],2):
...   print (''.join(s))
ll
lo
lv
le
ol
oo
ov
oe
vl
vo
vv
ve
el
eo
ev
ee
"""
    if n==0:
        yield []
    else:
        for i in range(len(items)):
            for ss in selections(items, n-1):
                yield [items[i]]+ss
 
def permutations(items):
    """ Yields all permutations of items.
Equivalent to all_combinations(items,len(items)).
 
>>> for p in permutations(['l','o','v','e']):
...   print (''.join(p))
love
loev
lvoe
lveo
leov
levo
olve
olev
ovle
ovel
oelv
oevl
vloe
vleo
vole
voel
velo
veol
elov
elvo
eolv
eovl
evlo
evol
"""
    return all_combinations(items, len(items))
 
 
__test__ = {}
__test__['tests'] = """
>>> # Permutations of 'love'
>>> print (list(map(''.join, list(permutations('done')))))
['done', 'doen', 'dnoe', 'dneo', 'deon', 'deno', 'odne', 'oden', 'onde', 'oned', 'oedn', 'oend', 'ndoe', 'ndeo', 'node', 'noed', 'nedo', 'neod', 'edon', 'edno', 'eodn', 'eond', 'endo', 'enod']
"""
 
 
if __name__ == "__main__":
    print ('PyAnalysisUtils/combo.py test')
    import doctest
    doctest.testmod()